Here's a way to do it.
Let 4e +2 = 5n +1 . . . . . . for some integer n
Then e = (5n -1)/4 = n + (n -1)/4
We want (n-1)/4 to be an integer, so let it be integer m.
... m = (n -1)/4
... 4m = n -1
... 4m +1 = n
Substituting this into our expression for e gives
... e = (5(4m+1) -1)/4 = (20m +4)/4 = 5m +1
e = 5m+1 for any integer m
A: To find the rate in feet per minute, we can use the information given.
Every two minutes, the submarine dives 300 feet. So
.
In order to confirm that our rate is correct, we can use the second set of information given.
=
.
Since we know that the rate is 150 feet per minute, we can multiply it by any number of minutes and get the answer of how deep the submarine is. We can use a variable x to represent the number of minutes and y to represent the depth in feet.
There's our equation.
B: It would be more reasonable to use an equation with the rate feet per minute because it is more accurate since the time interval isn't too big.
Use pythagorean’s theorem
as you can see it’s a right isosceles triangle
so your equation is adapted to this:
p^2 + p^2=44^2
add like terms and simplify
2p^2=1936
divide by 2
p^2=968
square root
p= √968
simplify
p=22√2
the answer would be your second option